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One class of investors will be only too glad to wave 2011 goodbye. If you had any money riding on overseas stock markets, chances are you’ve taken some pretty nasty lumps. This past year, the broadest measure of developed foreign markets, the iShares MSCI EAFE Index Fund (NYSE:EFA) lost 15.62% in dollar terms (excluding dividends).

The emerging bourses, according to the iShares MSCI Emerging Markets Index ETF (NYSE:EEM), fared even worse, skidding 21.12%. Painful indeed, especially when you consider that the headline U.S. stock indexes were either slightly above (Dow Jones industrials) or slightly below (S&P 500) the breakeven line.

So the question arises: Does it still make sense to diversify internationally? Or has another investment fairy tale gone “poof” at midnight?

Values Point to Profits Ahead

Tempting as it is to be cynical about a financial world that often seems broken, I don’t think we’ve seen the end of great profit-making opportunities in foreign markets. In fact, the recent weakness in overseas stocks is probably setting us up for exceptional returns once the current distress passes.

The main reason, of course, is valuation. As of mid-December, according to Bloomberg, the stocks in the Stoxx Europe 600 index were quoted at a slender 10.1 times estimated 2011 earnings, versus 12.2X for the Standard & Poor’s 500 index — a discount of 17%. The iShares MSCI Pacific ex-Japan Index (ETF) (NYSE:EPP), which normally trades at a sizable premium to the S&P because of Asia’s superior economic growth, was at 12.6X.

Some emerging markets are even cheaper. Brazi is selling for about 8X trailing 12 months’ earnings, and India about 12X — both well below their norms for the past five years. Remember also that despite a recent slowdown, these countries are still growing much faster than the developed economies of North America or Europe.

For the opening months of 2012, I’m taking a cautious view of most foreign stock markets. Europe’s sovereign debt travails will weigh on economic activity around the world, but especially in the EU homeland. In addition, we’re picking up early signs that China’s credit-fueled boom may be due for a setback in 2012. Chinese purchasing managers report that the country’s manufacturing sector is now contracting at the steepest rate since early 2009.

From North to South

Accordingly, I recommend that you proceed slowly and judiciously with new commitments. In Europe, I advise you to favor recession-resistant health care and consumer-staples names, such as drug maker Novartis (NYSE:NVS) and food processor Nestle (PINK:NSRGY). Not so coincidentally, both are based in Switzerland — with its friendly business climate and sound currency.

Both stocks also throw off generous dividend yields: 4.07% for NVS, and 3.41% for NSRGY. Dividends are typically paid once a year, in April. Switzerland extracts a 15% withholding tax on dividends remitted to U.S. shareholders, but you can obtain a credit against this tax if you hold the stock in a taxable account (not an IRA).

Among the other developed markets, my top choice is Australia, whose tax law encourages corporations to pay out the lion’s share of their profits in the form of dividends. As a result, most Australian stocks yield considerably more than their U.S. counterparts.

Take Westpac Banking (NYSE:WBK). Strong and conservatively managed, this Aussie bank has boosted its dividend more than 400%, in dollar terms, over the past 10 years. Current yield: a mouth-watering 7.8%. Dividends are paid semiannually, in July and December. No withholding tax is currently imposed on U.S. residents.

For a diversified portfolio of Australian stocks, consider iShares MSCI Australia Index Fund (ETF) (NYSE:EWA). This ETF owns a large slug of financials (44% of the portfolio), but it also gives you exposure to Australia’s natural-resources sector. Current yield: 4.71%.

Submerged, Not Sunk

Given that emerging markets have taken it on the chin, I’m confident that Brazil and India, my two longtime favorites among the developing bourses, will eventually snap back to their 2011 highs and beyond. Before a lasting turnaround can occur, however, investors will need to get a sense that the growth outlook in these countries is stabilizing.

That will take time. So, I suggest dribbling cash into vehicles like iShares MSCI Brazil Index (ETF) (NYSE:EWZ) and PowerShares India Portfolio (ETF) (NYSE:PIN) in equal-dollar installments over a period of three to six months.

For the immediate future, emerging-markets bonds seem to hold greater potential than stocks. Unlike U.S. Treasuries, EM bonds offer worthwhile yields that exceed, in most cases, the dividends you could earn on stocks from the same countries.

The J.P. Morgan U.S. Dollar Emerging Markets Bond Fund (NYSE:EMB) is the safest pick, suitable for virtually all investors. If you want to shoot for a little more income, go with TCW Emerging Markets Income Fund (MUTF:TGINX), which invests mainly in private-sector bonds rather than governments. Current yield: 6.94%.